Timeline for Computing the hopf invariant (without integration or homology, as in Milnor) of the hopf map
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| Oct 18, 2010 at 4:28 | comment | added | Andy Putman | It's pretty standard stuff. I recommend looking at page 132 of Dale Rolfsen's "Knots and Links", which lists 8 different definitions of linking numbers for knots in $S^3$. It is a useful test of your knowledge of algebraic topology to determine which of them generalize to give a linking pairing between cycles of the appropriate dimensions in $S^n$. | |
| Oct 18, 2010 at 3:55 | comment | added | Harry Gindi | @Andy: Having taken both of the first-year grad courses in topology here, I can say for sure that we did not discuss linking numbers. | |
| Oct 18, 2010 at 3:53 | comment | added | Harry Gindi | @Andy: Be that as it may, I just answered a question on Noether normalization that was substantially easier than this question. | |
| Oct 18, 2010 at 3:26 | comment | added | Andy Putman | Atiyah-MacDonald and Milnor's "Topology from the Differentiable Viewpoint" are at similar levels (1st year grad), though Milnor is maybe a little easier. However, AM contains a couple of exercises that are notoriously difficult (even for experts) and thus are borderline appropriate. Milnor does not, and what you asked is absolutely standard 1st year graduate topology. | |
| Oct 18, 2010 at 1:36 | vote | accept | Harry Gindi | ||
| Oct 18, 2010 at 1:08 | comment | added | Harry Gindi | People have asked problems from Atiyah-MacDonald here before, and this is certainly more research-level than those. | |
| Oct 18, 2010 at 0:35 | comment | added | Andy Putman | This is not research level. I voted to close. | |
| Oct 18, 2010 at 0:02 | history | edited | Harry Gindi | CC BY-SA 2.5 |
edited title
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| Oct 17, 2010 at 23:59 | comment | added | Harry Gindi | Sure, but integration is not covered in the book, and all of the other exercises only use material covered in the book. | |
| Oct 17, 2010 at 23:52 | answer | added | Dylan Thurston | timeline score: 3 | |
| Oct 17, 2010 at 23:45 | comment | added | Ryan Budney | The degree of a map $f : M \to N$ provided $M$ and $N$ are compact, orientable and of the same dimension is given by an integral. Think about $\int_M f^* \omega$, provided $\int_N \omega = 1$. | |
| Oct 17, 2010 at 23:36 | history | asked | Harry Gindi | CC BY-SA 2.5 |